Numerous disposable dispensing cartons and containers have previously been utilized to dispense paper products such as napkins, facial tissue, towels, wipes and so forth. These dispensing cartons have been provided with various dispensing ports and configurations to enhance the display and/or dispensing of the paper products contained therein. However, many disposable dispensing cartons are capable of providing reliable dispensing only when there is little or no pressure or weight bearing upon the sheet to be dispensed. Accordingly, disposable dispensing cartons that dispense the pressure-bearing sheet can suffer from poor or inadequate dispensing. In this regard, it is noted that dispensing through a lower portion of the dispenser requires removal of a sheet that is bearing the weight of the over-lying paper products. As examples, problems associated with dispensing pressure-bearing sheets include the formation of unwanted tears or tabs in the sheets and loss of sheet leads (i.e. the exposed portion of the next sheet to be dispensed that extends outwardly from the dispensing aperture). Dispensing difficulties of this nature can be further increased by high capacity dispensing cartons that have increased numbers of paper products. Thus, there exists a need for disposable dispensing cartons configured to reliably dispense pressure-bearing sheets, such as through a lower portion of the dispenser, and that are capable of providing reliable dispensing even when using significant numbers of paper products.